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For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the v{C}ech-de Rham complex. In addition, explicit formulas for such primitive family are presented.
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory
We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from
The classical Hochschild--Kostant--Rosenberg (HKR) theorem computes the Hochschild homology and cohomology of smooth commutative algebras. In this paper, we generalise this result to other kinds of algebraic structures. Our main insight is that produ
We show that Hidas families of $p$-adic elliptic modular forms generalize to $p$-adic families of Jacobi forms. We also construct $p$-ad
Let Y and X denote C^k vector fields on a possibly noncompact surface with empty boundary, k >0. Say that Y tracks X if the dynamical system it generates locally permutes integral curves of X. Let K be a locally maximal compact set of zeroes of X.